The home side threatened in the opening stages of the match when Joshua Risdon latched on to a loose ball on the edge of the box, but he could only drive his effort wide of the target.
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Sydney rallied when Alex Gersbach lifted the ball over the top of the Perth defence for the run of Filip Holosko, who tried to lob the ball over the on-rushing Ante Covic, but the keeper was able to claim the ball.
Moments later, Chris Harold cut inside from the flank before curling straight at the goalkeeper, while the striker fired into the side-netting just short of the hour mark.
Sydney had been on the back foot but as the game headed into the final quarter, Matt Simon wasted a good chance inside the box, heading wide from Gersbach's cross.
Harold could have won it for Perth in the closing stages, but after his lob had cleared the bar, chances were few and far between, allowing Sydney to move to within two points of top spot in the league table.